Convexity is a measure of the curvature in the relationship between bond prices and bond yields. It demonstrates how the duration of a bond changes as the interest rate changes. This is important because when interest rates change, the price does not change linearly, but rather it changes along the curve. In theory, as the yield decreases, the price of the bond increases at an increasing rate. This is due to the convex nature of the price-yield relationship. In practice, this means that when interest rates decrease, the price of a bond will increase more than it would have if the relationship was linear. Therefore, the effect of convexity is to decrease bond yields both in theory and in practice.

Choice A is incorrect. Convexity does not increase bond yields in theory or practice. In fact, the opposite is true. The concept of convexity suggests that as interest rates decrease, the price of a bond increases at an increasing rate. This implies a decrease in yield due to the inverse relationship between price and yield.

Choice C is incorrect. While it's true that convexity theoretically leads to lower yields (not higher), this effect may not always be observed in practice due to market imperfections and other factors such as liquidity risk, credit risk etc.

Choice D is incorrect. This choice incorrectly suggests that convexity decreases bond yields only in theory but not in practice which contradicts with the concept of convexity where it impacts both theoretical and practical scenarios.

Things to Remember

• Convexity is a key concept in fixed income analysis and risk management.
• It measures the sensitivity of a bond's duration to changes in interest rates.
• Convexity helps to provide a more accurate estimate of the bond's price change in response to interest rate movements.
• Higher convexity implies that the bond's price is more sensitive to changes in interest rates.
• Convexity is particularly important when analyzing bonds with embedded options.